Functional Gradient Optimization for Manipulation · PowerPoint Presentation Author: Siddhartha...
Transcript of Functional Gradient Optimization for Manipulation · PowerPoint Presentation Author: Siddhartha...
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CHOMP
Functional Gradient Optimization for Manipulation
Siddhartha Srinivasa Associate Professor
Robotics Institute, CMU Director
Personal Robotics Lab
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Motion
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Motion Optimal
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Optimal Motion with Functional Gradient Optimization
CHOMP: Covariant Hamiltonian Optimization for Motion Planning. Zucker, Ratliff, Dragan, Pivtoraiko,
Klingensmith, Dellin, Bagnell, Srinivasa International Journal of Robotics Research (IJRR) 2013.
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Three spaces of manipulation planning
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QW Ξξ
ξ
q
3 dimensions N dimensions ∞ dimensions
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12
tξ1+tξA
∞ dimensions
Ξ
Infinite Dimensional Hilbert Space
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Cost Functional
The Smoothness Cost The Obstacle Cost
W
ICRA’09: Ratliff et. al CHOMP: Gradient Optimization Techniques for Efficient Motion Planning
A
][][][ ξξλξ obssmooth ffU +=
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Optimizing the functional gradient of U
first order approximation of U regularization
smoothness metric
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Covariant Functional Gradient Update
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CHOMP:Realtime
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CHOMP:Realtime
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Local minima
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widening good
basins
initializing in good basins
Alleviating the local minima problem
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Make the problem easier by taking advantage of the natural flexibility in manipulation.
ICRA’11: Dragan et. al Manipulation Planning with Goal Sets Using Constrained Trajectory Optimization
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Goal sets
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Goal sets
goal set for placing bowl on the dinner table
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Ξ
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Q
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Optimal Motion with Functional Gradient Optimization
CHOMP: Covariant Hamiltonian Optimization for Motion Planning. Zucker, Ratliff, Dragan, Pivtoraiko,
Klingensmith, Dellin, Bagnell, Srinivasa International Journal of Robotics Research (IJRR) 2013
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Motion Optimal
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CHOMP
Functional Gradient Optimization for Manipulation
Siddhartha Srinivasa Associate Professor
Robotics Institute, CMU Director
Personal Robotics Lab